authors/mapgccv/finance/efficient_frontier.ipynb

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      "source": [
        "### Efficient Frontier with Google Sheets\n",
        "[![efficient_frontier.ipynb](https://img.shields.io/badge/github-%23121011.svg?logo=github)](https://github.com/ampl/colab.ampl.com/blob/master/authors/mapgccv/finance/efficient_frontier.ipynb) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ampl/colab.ampl.com/blob/master/authors/mapgccv/finance/efficient_frontier.ipynb) [![Hits](https://h.ampl.com/https://github.com/ampl/colab.ampl.com/blob/master/authors/mapgccv/finance/efficient_frontier.ipynb)](https://colab.ampl.com)\n",
        "\n",
        "Description: Efficient Frontier example using Google Sheets\n",
        "\n",
        "Tags: amplpy, google-sheets, finance\n",
        "\n",
        "Notebook author: Christian Valente <<christian.valente@gmail.com>>\n",
        "\n",
        "Model author: Harry Markowitz\n",
        "\n",
        "References:\n",
        "1. Markowitz, H.M. (March 1952). \"Portfolio Selection\". The Journal of Finance. 7 (1): 77–91. doi:10.2307/2975974. JSTOR 2975974."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q72dLDiaRoZ5"
      },
      "source": [
        "### Install needed modules and authenticate user to use google sheets"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "aKiYKyDUEOyV"
      },
      "outputs": [],
      "source": [
        "from google.colab import auth\n",
        "\n",
        "auth.authenticate_user()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JVIEGBHREh59",
        "outputId": "89ef87af-c9ad-4575-c3ad-eba1daf8a10d"
      },
      "outputs": [],
      "source": [
        "# Install dependencies\n",
        "%pip install -q amplpy gspread --upgrade"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 431,
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        },
        "id": "QFXXgRbZEon0",
        "outputId": "c0388b8a-cf25-4437-cf81-96751f0e7f2d"
      },
      "outputs": [],
      "source": [
        "# Google Colab & Kaggle integration\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"cplex\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register magics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IDSkh0OQUFO0"
      },
      "source": [
        "### Auxiliar functions\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "RQJJ0oUNE4G4"
      },
      "outputs": [],
      "source": [
        "import gspread\n",
        "from google.auth import default\n",
        "\n",
        "creds, _ = default()\n",
        "gclient = gspread.authorize(creds)\n",
        "\n",
        "\n",
        "def open_spreedsheet(name):\n",
        "    if name.startswith(\"https://\"):\n",
        "        return gclient.open_by_url(name)\n",
        "    return gclient.open(name)\n",
        "\n",
        "\n",
        "import pandas as pd\n",
        "\n",
        "\n",
        "def get_worksheet_values(name):\n",
        "    return spreedsheet.worksheet(name).get_values(\n",
        "        value_render_option=\"UNFORMATTED_VALUE\"\n",
        "    )\n",
        "\n",
        "\n",
        "def table_to_dataframe(rows):\n",
        "    return pd.DataFrame(rows[1:], columns=rows[0]).set_index(rows[0][0])\n",
        "\n",
        "\n",
        "def matrix_to_dataframe(rows, tr=False, nameOverride=None):\n",
        "    col_labels = rows[0][1:]\n",
        "    row_labels = [row[0] for row in rows[1:]]\n",
        "\n",
        "    def label(pair):\n",
        "        return pair if not tr else (pair[1], pair[0])\n",
        "\n",
        "    data = {\n",
        "        label((rlabel, clabel)): rows[i + 1][j + 1]\n",
        "        for i, rlabel in enumerate(row_labels)\n",
        "        for j, clabel in enumerate(col_labels)\n",
        "    }\n",
        "    df = pd.Series(data).reset_index()\n",
        "    name = nameOverride if nameOverride else rows[0][0]\n",
        "    df.columns = [\"index1\", \"index2\", name]\n",
        "    return df.set_index([\"index1\", \"index2\"])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MtozkvNhUcPj"
      },
      "source": [
        "### Efficient Frontier Example"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GV_i-6_HQvIA"
      },
      "source": [
        "Open connection to the spreadsheet and get the data, using the utility functions in ampltools to get pandas dataframes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "yCI9AMVFE4B3"
      },
      "outputs": [],
      "source": [
        "spreedsheet = open_spreedsheet(\n",
        "    \"https://docs.google.com/spreadsheets/d/1d9wRk2PJgYsjiNVoKi1FcawGSVUB5mxSeQUBdEleUv4/edit?usp=sharing\"\n",
        ")\n",
        "\n",
        "rows = get_worksheet_values(\"covariance\")\n",
        "# To be able to use ampl.set_data, we override the data column\n",
        "# of the dataframe to the name of the parameter we will be setting (S)\n",
        "covar = matrix_to_dataframe(rows, nameOverride=\"S\")\n",
        "\n",
        "rows = get_worksheet_values(\"expectedReturns\")\n",
        "expected = table_to_dataframe(rows)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "25oT2-OQRnjh"
      },
      "source": [
        "The following is a version of Markowitz mean-variance model, that can be used to calculate the efficient frontier"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "pLtarkfFK2Rl"
      },
      "outputs": [],
      "source": [
        "%%ampl_eval\n",
        "\n",
        "set A ordered;         # assets\n",
        "\n",
        "param S{A, A};         # cov matrix\n",
        "param mu{A} default 0; # expected returns\n",
        "param lb default 0;\n",
        "param ub default Infinity;\n",
        "param targetReturn default -Infinity;\n",
        "\n",
        "var w{A} >= lb <= ub;  # weights\n",
        "var portfolioReturn >= targetReturn;\n",
        "\n",
        "minimize portfolio_variance: sum {i in A, j in A} S[i, j] * w[i] * w[j];\n",
        "maximize portfolio_return: sum{a in A} mu[a] * w[a];\n",
        "\n",
        "s.t. def_total_weight: sum {i in A}  w[i] = 1;\n",
        "s.t. def_target_return: sum{a in A} mu[a] * w[a] >= targetReturn;"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yqurA6V9SWjf"
      },
      "source": [
        "Using amplpy we set the data of the ampl entities using the dataframes we got from google sheets"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "OODUiL4OVEVt"
      },
      "outputs": [],
      "source": [
        "# Set expected returns\n",
        "ampl.set_data(expected, set_name=\"A\")\n",
        "# Set covariance data\n",
        "ampl.set_data(covar)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q-IKUOv4Sfsl"
      },
      "source": [
        "Set a few options in AMPL to streamline the execution"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "0KxgnB0taV6O"
      },
      "outputs": [],
      "source": [
        "%%ampl_eval\n",
        "# Set options\n",
        "option solver cplex;\n",
        "option solver_msg 0;\n",
        "\n",
        "# The following declarations are needed for the efficient frontier script\n",
        "param nPoints := 20;\n",
        "param minReturn;\n",
        "param maxReturn;\n",
        "param variances{1..nPoints+1};\n",
        "param returns{1..nPoints+1};\n",
        "param delta = (maxReturn-minReturn)/nPoints;"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_Bpvh1ecT8z2"
      },
      "source": [
        "Calculate the extreme points for the efficient frontier procedure: get the minimum return by solving the min varance problem, then get the maximum return by solving the max return problem."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pYG0mQrWNOwJ",
        "outputId": "44083eb0-f50c-488a-8db9-d841c5c65fde"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Min portfolio variance: 0.000092, return: 0.001530\n",
            "Max portfolio variance: 0.000249, return: 0.002182"
          ]
        }
      ],
      "source": [
        "%%ampl_eval\n",
        "# Solve the min variance problem to get the minimum return\n",
        "objective portfolio_variance;\n",
        "solve > NUL;\n",
        "printf \"Min portfolio variance: %f, return: %f\\n\", portfolio_variance, portfolio_return;\n",
        "\n",
        "let minReturn := portfolio_return;\n",
        "# Store the first data point in the efficient frontier\n",
        "let variances[1] := portfolio_variance;\n",
        "let returns[1] := minReturn;\n",
        "\n",
        "# Solve the max return problem\n",
        "objective portfolio_return;\n",
        "solve > NUL;\n",
        "printf \"Max portfolio variance: %f, return: %f\", portfolio_variance, portfolio_return;\n",
        "let maxReturn := portfolio_return;"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uonczgPUUXeL"
      },
      "source": [
        "Now that we have the upper and lower values for the expected returns, iterate `nPoints` times setting the desired return at regularly increasing levels and solve the min variance problem, thus getting the points (return - variance) needed to plot the efficient frontier."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RDpBr66uB8F1",
        "outputId": "9b7dc599-bbee-49d9-b52b-f1f88efed61b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Return 0.001563, variance 0.000092\n",
            "Return 0.001596, variance 0.000092\n",
            "Return 0.001628, variance 0.000092\n",
            "Return 0.001661, variance 0.000093\n",
            "Return 0.001693, variance 0.000093\n",
            "Return 0.001726, variance 0.000094\n",
            "Return 0.001758, variance 0.000094\n",
            "Return 0.001791, variance 0.000095\n",
            "Return 0.001823, variance 0.000096\n",
            "Return 0.001856, variance 0.000097\n",
            "Return 0.001889, variance 0.000099\n",
            "Return 0.001921, variance 0.000100\n",
            "Return 0.001954, variance 0.000101\n",
            "Return 0.001986, variance 0.000104\n",
            "Return 0.002019, variance 0.000110\n",
            "Return 0.002051, variance 0.000118\n",
            "Return 0.002084, variance 0.000129\n",
            "Return 0.002116, variance 0.000144\n",
            "Return 0.002149, variance 0.000182\n",
            "Return 0.002182, variance 0.000249\n"
          ]
        }
      ],
      "source": [
        "%%ampl_eval\n",
        "\n",
        "# Switch objective to portfolio variance\n",
        "objective portfolio_variance;\n",
        "\n",
        "# Set starting point\n",
        "let targetReturn := minReturn;\n",
        "# Calculate the efficient frontier\n",
        "for{j in 1..nPoints}\n",
        "{\n",
        "\tlet targetReturn := targetReturn+delta;\n",
        "  solve > NUL;\n",
        "  printf \"Return %f, variance %f\\n\", portfolio_return, portfolio_variance;\n",
        "  let returns[j+1] := portfolio_return;\n",
        "\tlet variances[j+1]:=portfolio_variance;\n",
        "};"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3VjN2AhoU0FT"
      },
      "source": [
        "Finally, we plot the efficient frontier"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "-ULeZTu8Oh_Q",
        "outputId": "c1f40d8e-f50c-457c-c267-99c30fa604b0"
      },
      "outputs": [
        {
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PViZDfz/1jqP4+NsmcMggD/01s9w5ofRir6yv4cu/fJGnVm9m1KC+XHHesXz4dA/9NbP2cULphXbXNfDdh5bzo0dWMqhfKf9x/vHMOnWMh/6aWYc4ofQyv1+2gat+/SJrN+9m1qlj+NJ7j2P4gPJih2VmPYATSi+xfvsevnb3Eha98AZHjRrA/DlncMaRI4odlpn1IE4oPVxDY/DTJ9bwX/cuo66hkc+/+2jmvONI+pa6ecvM8ssJpQd7cd02vvTLF3i+ahtnTR7J12ce7yHAZlYwTig90I7aer593zJu/dNqhg/oy3cvPpn3n3i47243s4JyQulBIoJ7l7zBVxe+xPqaPXzk9HF84dxjGdLfw4DNrPCcUHqIqi27+Mqvl/Dgyxs49rBB3Ph3p3DKuGHFDsvMehEnlG5ub0Mj8x5dxX8/sByAL733WD7+tomU+SmJZtbJnFC6sZo9e/nkTxbzxMrNvOu4Q/nazKmMHtq/2GGZWS/lhNJNVe+o5ZIfP8XLr9fw7Qvfwt+eOqbYIZlZL+eE0g2t27qbj978JOu27OZHfz+Ndx57SLFDMjOjoA3tkmZIWiapUtIVzazvK+mOdP2TkiZkrLsyLV8m6dy0bKyk30t6SdISSf+cUX+4pPslLU9/9sge6RUbd3Dh9//Exppafvp/TncyMbMuo2AJRVIJcANwHjAFuFjSlKxqlwJbImIScB1wbbrtFGA2MBWYAdyY7q8e+HxETAHOAC7L2OcVwIMRMRl4MH3fo7y4bhsX/uBx6hoamT/nDE6bMLzYIZmZ7VPIK5TpQGVErIyIOmA+MDOrzkzg1nT5TuAcJXffzQTmR0RtRKwCKoHpEfF6RDwLEBE1wFJgdDP7uhU4v0DnVRRPrKxm9twn6F9Wwv/+w1uZeoSfnmhmXUshE8poYG3G+yr2f/m/qU5E1APbgBG5bJs2j50MPJkWHRoRr6fLbwCHNheUpDmSFktavHHjxoM7oyJ54KX1/P28pzhsSD/u/PSZTPT0KWbWBXXLmxUkDQR+AXw2IrZnr4+IAKK5bSNibkRMi4hpo0aNKnCkHffLP1fxqZ8+w3GHDWLBp87k8CEeFmxmXVMhE8o6YGzG+zFpWbN1JJUCQ4Dq1raVVEaSTH4WEXdl1Fkv6fC0zuHAhrydSZH8+LFV/Msdf+H0icP52SfP8HNLzKxLK2RCeRqYLGmipHKSTvaFWXUWApeky7OAh9Kri4XA7HQU2ERgMvBU2r9yM7A0Ir7Tyr4uAX6d9zPqJBHBfz/wCl+7+yXeM+VQ5n3sNAb29QhvM+vaCvYtFRH1ki4H7gVKgHkRsUTS1cDiiFhIkhxuk1QJbCZJOqT1FgAvkYzsuiwiGiS9Hfgo8IKk59JDfSkiFgHfABZIuhRYA3yoUOdWaHc//zr//cByZp06hm988ARKPY2KmXUDSi4IWqkgHQ18ARhPRgKKiL8ubGiFN23atFi8eHGxwzhAbX0D53z7YQb3K+M3//h2+vTxlPNm1rVIeiYipmWX53KF8r/AD4AfAQ35DswO9NMnXqVqy25+8okTnEzMrFvJJaHUR8T3Cx6JsW33Xr730HLOmjySvzq6649AMzPLlEvj/N2SPiPp8HR6k+GSfIt2Afzg4RVs2bWXL844ttihmJkdtFyuUJpGTn0hoyyAI/MfTu/1+rbdzHt0FeefdATHj/Zd8GbW/bSaUCT1Aa6IiDs6KZ5e67r7XyECPv+eY4odiplZu7Ta5BURjRx4ZWIFsOyNGu58poq/P3M8Y4dXFDscM7N2yaUP5QFJ/5pOHe8+lAK49ncvM6BvKZe9c1KxQzEza7dc+lAuSn9ellHmPpQ8eWJlNQ+9vIEvzjiWYZ5axcy6sTYTSkRM7IxAequb/riKQwb15eNvm1DsUMzMOqTNhCLp75srj4if5D+c3qWuvpHHV2zi/JNH06+spNjhmJl1SC5NXqdlLPcDzgGeBZxQOuiZNVvYWdfgmxjNrEfIpcnrHzPfSxpK8vRF66BHlm+ktI9461Ejih2KmVmHtWca252A+1Xy4JFXNnLKuGEM6ldW7FDMzDoslz6Uu9n/9MM+wBSSCSOtAzbW1LLkte3863uOLnYoZmZ5kUsfyrcyluuBNRFRVaB4eo1HK5Pn2bv/xMx6ilyavN4bEQ+nr8ciokrStQWPrId75JVNDB9QzvFHeN4uM+sZckko726m7Lx8B9KbNDYGf1y+ibdPGulnnphZj9Fik5ekTwOfAY6U9HzGqkHAY4UOrCdb+sZ2Nu2odXOXmfUorfWh/Bz4LfCfwBUZ5TURsbmgUfVwjy7fBMBZk0cWORIzs/xpsckrIrZFxOqIuBgYC/x1RKwB+kjysOEO+NOKaiYdMpBDB/crdihmZnnTZh+KpK8AXwSuTIvKgZ8WMqiebG9DI0+v3syZR/pmRjPrWXLplL8A+ADJDY1ExGsk/SjWDs9XbWNXXYPvjjezHieXhFIXEUF6c6OkAbnuXNIMScskVUq6opn1fSXdka5/UtKEjHVXpuXLJJ2bUT5P0gZJL2bt6y2SHpf0gqS7JQ3ONc7O9PiKpP/kdF+hmFkPk0tCWSDph8BQSZ8EHgRuamsjSSXADSRDjKcAF0uaklXtUmBLREwCrgOuTbedAswGpgIzgBvT/QHckpZlu4nkccUnAL+kiz5p8vGV1Rx72CCG+9knZtbDtJlQIuJbwJ3AL4BjgP8bEd/NYd/TgcqIWBkRdSQTSs7MqjMTuDVdvhM4R5LS8vkRURsRq4DKdH9ExCNAc6PMjgYeSZfvB/42hxg7VW19A4tXb+GtR3l0l5n1PK0mFEklkkZGxP0R8QXgS8BESUtz2PdoYG3G+6q0rNk6EVEPbANG5LhttiXsT1gXkoxMexNJcyQtlrR448aNOZxG/vz51a3U1jdypvtPzKwHajGhSJpNciXwvKSHJb0HWEnShPWRTorvYHwC+IykZ0gGDdQ1Vyki5kbEtIiYNmpU595Y+KcV1fQRTJ84vFOPa2bWGVq7sfHLwKkRUSnpFOBxYFZE3J3jvtdx4FXCmLSsuTpVkkqBIUB1jtseICJeBt4DIOlo4G9yjLPTPLGimuNHD2FIf09Xb2Y9T2tNXnURUQkQEc8Cyw8imQA8DUyWNFFSOUkn+8KsOguBS9LlWcBD6YiyhcDsdBTYRGAy8FRrB5N0SPqzD0ky/MFBxFpwe/Y28NzarZzh0V1m1kO1doVyiKTPZbwfmvk+Ir7T2o4jol7S5cC9QAkwLyKWSLoaWBwRC4GbgdskVZI0r81Ot10iaQHwEsmU+ZdFRAOApNuBs4GRkqqAr0TEzSSjyC5LD38X8OPcPoLO8XzVNuoaGjltgpu7zKxnai2h/IgDb2DMft+miFgELMoquypjeQ9JB3pz214DXNNM+cUt1L8euP5g4utMT69OBqadOn5YkSMxMyuMFhNKRHytMwPp6Rav3sykQwb6/hMz67Ha80x5O0iNjcEza7Zw2gRfnZhZz+WE0gmWb9jB9j31TBvv/hMz67mcUDpBU/+JO+TNrCdr7YmNn2tpHbQ9ysv2W7x6M6MG9WXs8P7FDsXMrGBaG+XVNKLrGOA09t9D8n7auCfEDvT06qT/JJmmzMysZ2pzlJekR4BTIqImff9V4J5Oia4HeH3bbtZt3c2lb/dDLs2sZ8ulD+VQDpwXqy4tsxw8u2Yr4PtPzKzna63Jq8lPgKck/TJ9fz77p5y3NvylaivlJX047vAu+bwvM7O8aTOhRMQ1kn4LnJUWfTwi/lzYsHqO59ZuZcoRgykv9YA6M+vZcv2WqwC2p9ObVKUTNlob6hsaeaFqGyeNHVrsUMzMCq7NhCLpK8AXgSvTojLgp4UMqqdYvmEHu/c2OKGYWa+QyxXKBcAHgJ0AEfEaBzlJZG/1l7VJh7wTipn1BrkklLr0GSUBIGlAYUPqOZ5bu5Uh/csYP6Ki2KGYmRVcLgllgaQfkjwP5ZPAA8BNhQ2rZ3hu7VbeMnaob2g0s14hl1Fe35L0bmA7yV3zV0XE/QWPrJvbWVvPK+treM/Uw4odiplZp2gzoUi6NiK+CNzfTJm14MV122gMOGnskGKHYmbWKXJp8np3M2Xn5TuQnuaFddsAOGG0O+TNrHdobbbhTwOfAY6S9HzGqkHAnwodWHf30mvbOWRQX0YN6lvsUMzMOkVrTV4/B34L/CdwRUZ5TURsLmhUPcCS17Yz9QhPt2JmvUeLTV4RsS0iVgPXA5sjYk1ErAHqJZ3eWQF2R3v2NlC5cQdTj3D/iZn1Hrn0oXwf2JHxfkda1iZJMyQtk1Qp6Ypm1veVdEe6/klJEzLWXZmWL5N0bkb5PEkbJL2Yta+TJD0h6TlJiyVNzyXGQnhlfQ0NjeErFDPrVXJJKEpvbAQgIhrJbXRYCXADSQf+FOBiSVOyql0KbImIScB1wLXptlOA2cBUYAZwY7o/gFvSsmzfBL4WEScBV6Xvi2LJa9sBmOKEYma9SC4JZaWkf5JUlr7+GViZw3bTgcqIWBkRdcB8YGZWnZnsnwr/TuAcJXcBzgTmR0RtRKwCKtP9ERGPAM314QTQ9A0+BHgthxgLYslr2xjUt5Sxw3yHvJn1HrkklH8A3gqsA6qA04E5OWw3Glib8b4qLWu2TkTUA9uAETlum+2zwH9JWgt8i/2TWR5A0py0SWzxxo0bcziNg7fkte0cd8Rg+vTxHfJm1nu0mVAiYkNEzI6IQyLi0Ij4cERs6IzgDtKngX+JiLHAvwA3N1cpIuZGxLSImDZq1Ki8B9HQGLz8eo37T8ys18ll+vqjJT3Y1Aku6URJX85h3+uAsRnvx6RlzdaRVErSVFWd47bZLgHuSpf/l7SJrLOt2rST3XsbPMLLzHqdXJq8fkTSfLQXICKeJ+kwb8vTwGRJEyWVp9sszKqzkCQRAMwCHkoHACwEZqejwCYCk4Gn2jjea8A70uW/BpbnEGPeLXujBoBjD/MM/2bWu+TyTPmKiHgqa8bc+rY2ioh6SZcD9wIlwLyIWCLpamBxRCwkaZa6TVIlSUf77HTbJZIWAC+lx7osIhoAJN0OnA2MlFQFfCUibgY+CVyfXunsIbd+nrxbtr6GPoJJhwwsxuHNzIoml4SySdJR7H8eyizg9Vx2HhGLgEVZZVdlLO8BLmxh22uAa5opv7iF+o8Cp+YSVyEtX1/D+BED6FdW0nZlM7MeJJeEchkwFzhW0jpgFfCRgkbVjb2yvobJvjoxs14ol+ehrATelT6psU9E1BQ+rO6ptr6B1dW7OO/4w4sdiplZp8tllNcISd8F/gj8QdL1kkYUPrTuZ+XGnTQ0Bke7Q97MeqFcRnnNBzYCf0syEmsjcEchg+quXlmfXLwdfaibvMys98mlD+XwiPh6xvv/kHRRoQLqzpav30FpH3HkSCcUM+t9crlCuU/SbEl90teHSIYCW5Zl62uYMHIA5aW5fKxmZj1LLt98nyR52FZt+poPfEpSjaTthQyuu1m+vsbNXWbWa+Uyl9egiOgTEWXpq09aNigiPGFVqq6+kbVbdnPUKCcUM+udchnldWnW+xJJXylcSN3T2i27aGgMJo4cUOxQzMyKIpcmr3MkLZJ0uKTjgScAj4vNsmrjTgAnFDPrtXK5sfHD6aiuF4CdwIcj4rGCR9bNrNrkhGJmvVsuTV6TgX8GfgGsAT4qyY8izLKqeifDKsoYWlFe7FDMzIoilyavu4H/GxGfIpkefjnJ1PSWYdXGnb46MbNeLZcbG6dHxHaA9Fkl35Z0d2HD6n5WbdrJ2yaNLHYYZmZF0+IViqR/A4iI7ZKyp5j/WCGD6m521tbzxvY9HDnKVyhm1nu11uSV+VTGK7PWzShALN3W6mp3yJuZtZZQ1MJyc+97tdWbdgEwYYQTipn1Xq0llGhhubn3vdraLUlCGTu8f5EjMTMrntY65d+SztUloH/GvF0C+hU8sm6kassuhlaUMahfWbFDMTMrmhYTSkT4oeg5qtqymzHDfHViZr2b51nPg7WbdzFmqO/1NLPeraAJRdIMScskVUq6opn1fSXdka5/UtKEjHVXpuXLJJ2bUT5P0gZJL2bt6w5Jz6Wv1ZKeK+S5NYkIqrbsdv+JmfV6BUsokkqAG4DzgCnAxZKmZJPIsQ8AAA8jSURBVFW7FNgSEZOA64Br022nkAxbnkoyRPnGdH8At9DMsOWIuCgiToqIk0imibkr7yfVjE076qitb2TMMF+hmFnvVsgrlOlAZUSsjIg6kgdzzcyqMxO4NV2+k2RmY6Xl8yOiNiJWAZXp/oiIR4DNLR003f5DwO35PJmWNI3wch+KmfV2hUwoo4G1Ge+r0rJm60REPbANGJHjti05C1gfEcubWylpjqTFkhZv3Lgxx122rGrLbgBfoZhZr9cTO+UvppWrk4iYGxHTImLaqFGjOnywKl+hmJkBuU0O2V7rgLEZ78ekZc3VqZJUCgwBqnPc9k3SfXwQOLX9YR+cqi27GVZRxoC+hfwozcy6vkJeoTwNTJY0UVI5SSf7wqw6C4FL0uVZwEPpjMYLgdnpKLCJwGTgqRyO+S7g5YioyssZ5GD9tj0cNsRXJ2ZmBUsoaZ/I5cC9wFJgQUQskXS1pA+k1W4GRkiqBD4HXJFuuwRYALwE/A64LCIaACTdDjwOHCOpKuuZ97PppM74Jm9s38Nhg/t25iHNzLqkgrbTRMQiYFFW2VUZy3uA7Knxm9ZdA1zTTPnFrRzvY+2Ntb3Wb9/DCaOHdPZhzcy6nJ7YKd9p6uob2bSjjkMHe2ozMzMnlA7YuKMWgMOGOKGYmTmhdMAb2/YAcJivUMzMnFA6Yv32JKEc4k55MzMnlI7wFYqZ2X5OKB2wvmYP5SV9GD6gvNihmJkVnRNKB2zYXsuoQX1J5qM0M+vdnFA6oHpnHSMH+urEzAycUDpk885aN3eZmaWcUDpg8446hg/wCC8zM3BCabeIYNPOOka4ycvMDHBCabeddQ3U1Te6ycvMLOWE0k6bd9QBOKGYmaWcUNqpemcyj5dHeZmZJZxQ2mnzzqYrFHfKm5mBE0q7VacJZYSbvMzMACeUdtu6K0koQyvKihyJmVnX4ITSTtt319NHMLBvQR96aWbWbTihtNP2PXsZ3L/M83iZmaWcUNpp++69DO7n5i4zsyZOKO1Us6eeQf3c3GVm1sQJpZ227/EViplZpoImFEkzJC2TVCnpimbW95V0R7r+SUkTMtZdmZYvk3RuRvk8SRskvdjM/v5R0suSlkj6ZqHOC5JO+cH9fYViZtakYAlFUglwA3AeMAW4WNKUrGqXAlsiYhJwHXBtuu0UYDYwFZgB3JjuD+CWtCz7eO8EZgJviYipwLfyfU6Ztu/ZyyBfoZiZ7VPIK5TpQGVErIyIOmA+yRd+ppnArenyncA5SoZNzQTmR0RtRKwCKtP9ERGPAJubOd6ngW9ERG1ab0O+TyhTzZ56N3mZmWUoZEIZDazNeF+VljVbJyLqgW3AiBy3zXY0cFbadPawpNOaqyRpjqTFkhZv3Lgx55PJVN/QyI5aN3mZmWXqSZ3ypcBw4AzgC8ACNXOTSETMjYhpETFt1KhR7TrQzroGwDc1mpllKmRCWQeMzXg/Ji1rto6kUmAIUJ3jttmqgLsi8RTQCIxsd/St2LM3SSj9y0vaqGlm1nsUMqE8DUyWNFFSOUkn+8KsOguBS9LlWcBDERFp+ex0FNhEYDLwVBvH+xXwTgBJRwPlwKa8nEmW3ekVSv8yJxQzsyYFSyhpn8jlwL3AUmBBRCyRdLWkD6TVbgZGSKoEPgdckW67BFgAvAT8DrgsIhoAJN0OPA4cI6lK0qXpvuYBR6bDiecDl6TJKe9273VCMTPLVtBOgIhYBCzKKrsqY3kPcGEL214DXNNM+cUt1K8D/q4j8eaqKaH0c5OXmdk+PalTvtPsSZu8KnyFYma2jxNKO+x2p7yZ2Zs4obSD+1DMzN7MCaUddqVNXv2cUMzM9nFCaQffh2Jm9mZOKO1QV98IQFmJPz4zsyb+RmyHhsbk9payEj/+18ysiRNKO9SnCaWkjxOKmVkTJ5R2aLpCKe3jj8/MrIm/Eduh6QrFFyhmZvs5obRDQ2MjpX1EM7Pjm5n1Wk4o7VDfGPTx5YmZ2QGcUNqhsTEodUIxMzuAE0o71DeGR3iZmWVxQmmHBl+hmJm9iR+K3g5TDh9M7d7GYodhZtalOKG0w+zp45g9fVyxwzAz61Lc5GVmZnnhhGJmZnnhhGJmZnnhhGJmZnlR0IQiaYakZZIqJV3RzPq+ku5I1z8paULGuivT8mWSzs0onydpg6QXs/b1VUnrJD2Xvt5byHMzM7MDFSyhSCoBbgDOA6YAF0uaklXtUmBLREwCrgOuTbedAswGpgIzgBvT/QHckpY157qIOCl9Lcrn+ZiZWesKeYUyHaiMiJURUQfMB2Zm1ZkJ3Jou3wmco2TGxZnA/IiojYhVQGW6PyLiEWBzAeM2M7N2KGRCGQ2szXhflZY1Wyci6oFtwIgct23O5ZKeT5vFhjVXQdIcSYslLd64cWNuZ2JmZm3qSTc2fh/4OhDpz28Dn8iuFBFzgbkAkjZKWtOZQWYYCWwq0rHb4tgOXleNC7pubF01LnBsbRnfXGEhE8o6YGzG+zFpWXN1qiSVAkOA6hy3PUBErG9alvQj4DdtBRgRo9qqUyiSFkfEtGIdvzWO7eB11big68bWVeMCx9ZehWzyehqYLGmipHKSTvaFWXUWApeky7OAhyIi0vLZ6SiwicBk4KnWDibp8Iy3FwAvtlTXzMzyr2BXKBFRL+ly4F6gBJgXEUskXQ0sjoiFwM3AbZIqSTraZ6fbLpG0AHgJqAcui4gGAEm3A2cDIyVVAV+JiJuBb0o6iaTJazXwqUKdm5mZvVlB+1DSobuLssquyljeA1zYwrbXANc0U35xC/U/2qFgO9/cYgfQCsd28LpqXNB1Y+uqcYFjaxclLUxmZmYd46lXzMwsL5xQzMwsL5xQCiCHOcz+StKzkuolzcpad4mk5enrkuxtixWbpJMkPS5pSXrz6EVdIa6M9YMlVUn6Xj7j6mhsksZJuk/SUkkvZc5XV+S4vpn+Wy6V9N10hoq8ySG2z6Wfx/OSHpQ0PmNdwf4G2htXoX//OxJbxvqC/Q3kLCL8yuOLZETbCuBIoBz4CzAlq84E4ETgJ8CsjPLhwMr057B0eVgXie1oYHK6fATwOjC02HFlrL8e+Dnwva7y75mu+wPw7nR5IFBR7LiAtwKPpfsoAR4Hzu7kz+ydTZ8F8GngjkL/DXQwroL9/nc0tkL/DRzMy1co+dfmHGYRsToingeyH0x/LnB/RGyOiC3A/bQ8EWanxhYRr0TE8nT5NWADkK8bQzvymSHpVOBQ4L48xZOX2JRMcloaEfen9XZExK5ix0UytL4fyRdXX6AMWE/+5BLb7zM+iydIbl6Gwv4NtDuuAv/+dyg2KPjfQM6cUPKvvfOQdXTbTtu/pOkkX0Yrih2XpD4k0+z8a55iydaRz+xoYKukuyT9WdJ/af+s2UWLKyIeB35P8r/s14F7I2JpnuJqT2yXAr9t57adFdc+Bfj971BsnfA3kLOeNJeXdYJ0RoLbgEsi4k1XC0XwGWBRRFTluRsgH0qBs4CTgVeBO4CPkdzQWzSSJgHHsf9/uPdLOisi/liEWP4OmAa8o7OP3ZqW4uoKv//NxNZl/gacUPLvoOchy9r27Kxt/5CXqPbvv72xIWkwcA/w7xHxRBeJ60zgLEmfIemjKJe0IyLe1KlZhNiqgOciYiWApF8BZ5CfhNKRuC4AnoiIHWlcvyX5HPOVUHKKTdK7gH8H3hERtRnbnp217R+6QFyF/P3vaGyF/hvIXbE6b3rqiyRJrwQmsr9zbWoLdW/hzZ3yq0g6I4ely8O7SGzlwIPAZ7vSZ5a17mPkv1O+I59ZSVp/VPr+xyTTCBU7rouAB9J9lKX/ru/vzM+M5KptBWlHd0Z5wf4GOhhXwX7/Oxpbof8GDuo8inXgnvwC3gu8kv7j/3t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              "<Figure size 432x288 with 1 Axes>"
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        "\n",
        "df = ampl.get_data(\"returns\", \"variances\").toPandas()\n",
        "plt.plot(df.variances * 1000, df.returns)\n",
        "plt.xlabel(\"Variance*1000\")\n",
        "plt.ylabel(\"Expected Return\")\n",
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